Really did'nt understand how they approached this

The Q boield down to is PR = QR? --> PR to be = QR --> Angle P = Angle Q. We know that Angle R is a Right angle. --> P+Q = 90. But d/n know their ratio.--> So, we need the co-ordinates of both the points P and Q to measure the length of PR /QR. No info is given about the Triangle PQR (i.e. is it a 30-60-90 triangle). But I understand that If we extend PR, QR is extended proportionately (right triangle theorem).

I would go with C, as neither of the statements is enough to have the slope of the traingle PQR.

OA:

Could somebody show the workings?

hey,
which part of the solutions above did you have a difficulty in following?
i'll be glad to explain it in a little more detail if you let me know.
cheers!

Consider point \(R\) as \(R(e, f)\)

Statement 1) \(C=3\)
From this statement you can draw a conclusion that \(e=3\) as QR is parallel to Y-axis. But we do not know the value of \(f\). So Insufficient.

Statement 2) \(B=-1\)
From this statement you can draw a conclusion that \(f=-1\) as PR is parallel to X-axis. But we do not know the value of \(e\). So Insufficient.

Together, we know that \(e=3 & f=-1\). So \(R(e,f) = R(3, -1)\)

Now you can find out the distance between P & R, and R & Q:
Dist between P & R = \(\sqrt{(-2-3)^2+(-1-(-1))^2}=5\)
Dist between Q & R = \(\sqrt{(3-3)^2+(4-(-1))^2}=5\)

So Statement 1 and 2 together are sufficient.
Remember, you don't need to calculate the distances to answer the questions. You just need to know if the distances can be calculated using Statement 1 and 2.

Questions? Shoot...

choice C is correct because when data from both statements is provided (that is the coordinates of both the points) it can be possible to determine the lengths of both the lines.

since it is given that QR is parallel to the y-axis and PR is parallel to x-axis, we can find the coordinates of point R.

the x coordinate for R will be the same as that of Q (which is point c)
and the y coordinate will be the same as that of P (which is point b)

therefore coordinates of R will be (c,b)

now in order to calculate the length of QR, we need the y coordinates of both Q and R.. that is points d and b.
(the x coordinates are not necessary since we know that the line is parallel to the y axis.)

similarly, to calculate the length of PR, we need the x coordinates of both P and R.. that is points a and c.
(the y coordinates are not necessary because we know that the line is parallel to x axis.)

thus if we know the numerical value of the points represented by a,b,c and d, we can find the lengths of both the lines (QR and PR).

now, if we know the lengths of both the lines, we can easily find the ratio and see whether or not it will be equal to 1.

if there is any particular statement in my explanation where you loose the flow or cannot understand, just let me know!

hope this helps!

cheers!